JEE Main

JEE Mains paper is conducted by CBSE board not by any IIT.

Around 5000 for general category. AIR-5k.

Paper of JEE Mains is not tough but they make one part tough out of the three parts. Like last year, the paper of maths was tough. Before last year, the paper of physics was tough. It is random. We can't predict anything.

The JAC Chandigarh takes care of admissions into PEC. Generally, admissions are done not only on the basis of JEE but also on class 12th percentage. So, if you have a good percentage in class 12th, you can get direct admission on the basis of the same.

Cutoff required in JEE Mains to get CSE in COEP:
To get into CS-IT, EnTC 188+ score is required, for mechanical, electrical it's 176+ etc.

No, you must score well in your 12th standard.

No, you cannot get admission in PEC without JEE Mains.

There is no home state quota for DAIICT. The seats in DAIICT are allocated as follows for the B.Tech course:
Out of the 300 seats, 150 seats are allocated through the state counselling process called ACPC and rest through All India Quota and NRI quota (~ 5%) for which a rank list is prepared based on the JEE Mains rank list which according to past trends lies around 15000.

Check out the link below and click on the college names to know their cutoff:
https://www.shiksha.com/b-tech/resources/jee-mains-cut-off-predictor
Also refer https://www.resonance.ac.in/reso/news/JEE-Main-Branch-Predictor.aspx.

Follow the link below :
Top colleges accepting JEE Mains https://www.shiksha.com/b-tech/ranking/top-engineering-colleges-in-india-accepting-jee-mains/44-2-0-0-6244
Top government colleges accepting JEE Advance score are mainly top IITs I.e IIT Bombay, IIT Madras, IIT Delhi, IIT Kharagpur etc.